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CN114154823B - Robust berth shore bridge joint distribution method based on improved particle swarm optimization - Google Patents

Robust berth shore bridge joint distribution method based on improved particle swarm optimization Download PDF

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CN114154823B
CN114154823B CN202111391031.0A CN202111391031A CN114154823B CN 114154823 B CN114154823 B CN 114154823B CN 202111391031 A CN202111391031 A CN 202111391031A CN 114154823 B CN114154823 B CN 114154823B
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杨玉
马金慧
戴红伟
戴迎春
贾东宝
李存华
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Abstract

The invention discloses a robust berth shore bridge joint distribution method based on an improved particle swarm algorithm, which comprises the following steps of S1: initializing a population; s2: calculating the earliest berthing time; s3: calculating the latest berthing time; s4: inserting a buffer area; s5: self-adaptive variation of particles; s6: calculating an objective function value of the sample; namely the delay departure time of the ship; s7: updating the individual optimal value and the global optimal value of the particle; s8: updating the speed and position of the particles; s9: letting TN = TN +1, judging whether a termination condition of reaching the maximum iteration number TN is met, if so, terminating iteration and outputting an optimal solution, otherwise, returning to the step S2 to continue iteration; the invention reduces the negative influence of uncontrollable factors such as delay of arrival of ships or prolongation of cargo loading and unloading time of ships caused by weather or equipment faults on the overall operation efficiency of the port, reduces economic cost and time cost, can quickly and effectively solve the berth shore bridge scheduling problem, and further improves the overall operation efficiency of the container terminal.

Description

Robust berth shore bridge joint distribution method based on improved particle swarm optimization
Technical Field
The invention relates to the field of transportation decision of sea-land combined transportation, in particular to a robust berth shore bridge combined distribution method based on an improved particle swarm algorithm.
Background
The berth and the shore bridge are used as important resources of the wharf, and have important influence on the production efficiency of the wharf. The berth is the area for ships to berth along the shore line of the wharf, and the shore bridge is an important tool for loading and unloading containers on the ships. Under the influence of uncertain factors such as severe weather and wharf facility faults, the arrival time, loading and unloading working time and the like of a ship can have certain uncertainty, and the uncertain factors often make a berth shore bridge scheduling plan in a tight coupling mode difficult to execute, so that the original berth shore bridge scheduling plan can be delayed or even interrupted, and the overall efficiency of a port is seriously influenced.
In the prior art, the influence of the fault of the shore bridge on the ship shore bridge scheduling scheme is considered, a model is constructed to obtain the optimal shore bridge re-scheduling scheme at each rolling stage decision point, but the influence of the accumulation of the shore bridge fault and the site bridge fault on the ship loading and unloading progress is not considered, and the shore bridge scheduling scheme of a single ship is only researched.
In the prior art, a berth-shore-bridge joint scheduling two-stage model considering berth preference and shore-bridge movement frequency is established. The first stage model adopts a variable arrival time strategy of ships, and establishes a mixed integer programming model with minimum cost as a target. In the second stage model, interference constraint of a quay crane is considered, an integer planning model with the minimal quay crane movement frequency as a target is established, and a berth-quay crane combined scheduling plan in a given planning period can be obtained, however, the situation that actual working conditions of berths and quay bridges and planned conditions come in and go out is not considered in the actual wharf operation process when the planning period is long. Although many models and algorithms for solving the problem of the berth shore bridge allocation are provided at present, and certain improvement is provided in the aspect of optimizing precision of the models and algorithms, the models and the methods for solving the problem of the berth shore bridge still need to be further improved in the case of large scale, long planning period and possible change of the actual environment.
In an actual berthing shore bridge operation scene, uncontrollable factors such as delay of ships arriving at a port or prolonging of cargo loading and unloading time of the ships may occur due to weather or equipment faults, and the occurrence of the unexpected factors can cause extra economic cost, time cost and the like, so that a robust berthing shore bridge scheduling scheme which can better cope with the influence of the uncertain factors is very important for relieving the negative influence of the uncertain factors on the overall operation efficiency of the port; therefore, the robust berth shore bridge joint distribution method based on the improved particle swarm optimization is provided.
Disclosure of Invention
The invention aims to provide a robust berth shore bridge joint distribution method based on an improved particle swarm algorithm aiming at the defects of the prior art so as to solve the problems provided by the background technology.
In order to achieve the purpose, the invention provides the following technical scheme: a robust berth shore bridge joint distribution method based on an improved particle swarm algorithm comprises the following specific steps:
s1: initializing a population; the method specifically comprises the steps of population scale, iteration times, upper and lower boundaries of particle positions and speeds, inertia weight and learning factors; the coding length is n =6 of the total number of ships: the ship number is: 1. 2, 3, 4, 5, 6; docking sequence O j Comprises the following steps: 1. 3, 5, 2, 4, 6; berthing x j Comprises the following steps: 2. 1,2, 3, 4; number y of quay bridges j Comprises the following steps: 3. 5, 2, 4, 1, 2;
s2: calculate the earliest berthing time tb j (ES): for vessel j, calculate tb j The formula (ES) is as follows:
Figure GDA0003915057640000021
wherein s is ijk The k-th berthing of the ship j at the berth i is 1, otherwise, the k-th berthing is 0 j Indicates the arrival time, td, of vessel j j' Represents the departure time of vessel j' at berth i;
s3: calculating the latest berthing time tb j (LS): for the ship j, if j' is the ship berthing at the same berth and the ship berthing at the next berth, t = tb is set j' (LS) if no such ship exists, let t = td j Calculating tb j The formula of (LS) is as follows:
Figure GDA0003915057640000022
wherein tw j Represents the working time of the ship j;
s4: inserting a buffer area;
s5: self-adaptive variation of particles; the PSO algorithm has strong global search capability and memory, has strong optimization capability in the early stage of iteration, is difficult to jump out of a local optimal solution to find a global optimal solution because of inevitable dropping into a local trap in the later stage of iteration, and is improved by designing the following adaptive variation strategy aiming at the characteristics of the PSO algorithm and a constructed berth shore bridge problem model, so that the updating formula of the adaptive variation probability P is as follows:
Figure GDA0003915057640000031
wherein TN is the current iteration frequency, and TN is the total iteration frequency; for the particle i, randomly generating a random number between 0 and 1, and if the random number is greater than the variation probability of the iteration, performing variation operation on the particle;
s6: calculating an objective function value of the sample; namely the time of delay departure of the ship, the formula is as follows:
Figure GDA0003915057640000032
s7: updating the individual optimal value and the global optimal value of the particle; for each particle, comparing the fitness value obtained by the iteration with the optimal fitness value pbest, if the fitness value is smaller than pbest, updating, and otherwise, keeping pbest unchanged; comparing pbest with the global optimum value gbest, and if the pbest is smaller than the gbest, replacing the gbest with the pbest;
s8: and updating the speed and the position of the particle, wherein the speed updating formula of the ith particle is as follows:
v ij (tn+1)＝wv ij (tn)+c 1 r 1j (p ij -x ij (tn))+c 2 r 2j (g j -x ij (tn)),j∈V
the location update formula is: x is the number of ij (tn+1)＝x ij (tn)+v ij (tn+1),j∈V
Wherein v is ij (tn + 1) represents the j-dimension velocity value of the tn +1 th iteration particle i, w is a weight coefficient, c 1 And c 2 As a learning factor, r 1j And r 2j For hybrids based on Logistic chaotic sequencesChaos variable, p ij Is the j-th dimension position value, g, of the optimal solution of the particle i j Position value of j dimension, x, being global optimum solution ij (tn) represents a j-dimensional position value of the particle i at the tn-th iteration; for the particles with updated speed and positions, carrying out boundary processing on the particles so as to enable the codes of the particles to meet the constraint;
s9: and (5) letting TN = TN +1, judging whether a termination condition of reaching the maximum iteration number TN is met, if so, terminating iteration and outputting an optimal solution, otherwise, returning to the step S2 and continuing iteration.
As a preferable embodiment of the present invention, O in S1 is j Representing the berthing sequence of the ship, and randomly arranging integers between 1 and n; x is the number of j Representing a berthing berth of the vessel; y is j Representing the number of shore bridges allocated to the vessel, is randomly generated between the minimum and maximum required number of shore bridges for the vessel, e.g. vessel 1 is first berthed at berth # 2 and is allocated 3 shore bridges.
As a preferred technical solution of the present invention, the specific steps of inserting the buffer zone in S4 are as follows:
s41: updating the weighting factor w j (ii) a The weighting factor represents the service priority of the ship, and if the weight coefficient exists, the calculated tb is used for j j (ES) and tb j Time and space conflicting vessels j' in the (LS) scheme, i.e. { x j ＝x j' ,tb j' (ES)＜tb j (ES)＜tb j' (LS)+tw j' If j, j' is equal to V }, then w j Set to 1, otherwise set to 0, where the set V = {1,2, \8230;, n };
s42: calculating the accumulated weight; calculating two key parameters alpha j 、β j The cumulative weight alpha of the ship j in the same berth and the ship in the previous port j And the cumulative weight beta of the ships at the port of the berth behind j ；
In the berth shore bridge scheme, not only the front and rear ships in transition but also other ships sharing the same wharf space need to be considered; thus, the definition set Fa (j) records the ship that is berthed at and ahead of the same berth as ship j, and the definition set Fb (j) records the ship that is berthed at and ahead of the same berth as ship jThe ship to be berthed later, defining W as the total weight of all ships, then
Figure GDA0003915057640000041
Calculating alpha j And beta j The formula of (1) is as follows:
Figure GDA0003915057640000042
s43: obtaining a more robust berth shore bridge scheme; the finally obtained berthing time tb of the ship inserted into the buffer area j From tb j (ES)、tb j (LS)、α j 、β j Obtaining:
Figure GDA0003915057640000051
as a preferred technical solution of the present invention, the mutation strategy in S5 is designed with two types, which are exchange and reverse order, specifically as follows: randomly selecting two columns for exchange; and (3) reversing the sequence: two columns are randomly selected from the sample, and the parts including the selected two columns and the parts between the two columns are arranged in the reverse order.
The invention has the beneficial effects that: the invention reduces the negative influence of uncontrollable factors such as delay of arrival of ships or prolongation of cargo loading and unloading time of ships caused by weather or equipment faults on the overall operation efficiency of the port, reduces economic cost and time cost, can quickly and effectively solve the berth shore bridge scheduling problem, and further improves the overall operation efficiency of the container terminal.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a comparison graph of index 1 and index 2 for different numbers of ships according to the present invention;
FIG. 3 is a schematic diagram of the mutation strategy of the present invention.
Detailed Description
The following detailed description of the preferred embodiments of the present invention, taken in conjunction with the accompanying drawings, will make the advantages and features of the invention more readily understood by those skilled in the art, and thus will more clearly and distinctly define the scope of the invention.
Referring to fig. 1, the present invention provides a technical solution: a robust berth shore bridge joint distribution method based on an improved particle swarm algorithm comprises the following specific steps:
s1: initializing a population; the method specifically comprises the steps of population scale, iteration times, upper and lower boundaries of particle positions and speeds, inertia weight and learning factors; taking 6 ships as an example, the coding length is n =6: the ship number is: 1. 2, 3, 4, 5, 6; docking sequence O j Comprises the following steps: 1. 3, 5, 2, 4, 6; berthing x j Comprises the following steps: 2. 1,2, 3, 4; number y of quay bridges j Comprises the following steps: 3. 5, 2, 4, 1, 2;
O j representing the berthing sequence of the ship, and randomly arranging integers from 1 to n; x is the number of j Representing a berthing of the vessel; y is j Representing the number of shore bridges allocated to the ship, randomly generated between the minimum and the maximum required number of shore bridges of the ship, such as the first berth of the ship 1 at No. 2, and 3 shore bridges allocated to the ship;
s2: calculate the earliest berthing time tb j (ES): for vessel j, calculate tb j The formula (ES) is as follows:
Figure GDA0003915057640000061
wherein s is ijk Indicating that the k-th berthing of the ship j at the berth i is 1, otherwise, the k-th berthing is 0 j Represents the time of arrival, td, of vessel j j' Represents the departure time of vessel j' at berth i;
s3: calculating the latest berthing time tb j (LS): for the ship j, if j' is the ship berthing at the same berth and the ship berthing at the next berth, t = tb is set j' (LS) if no such ship exists, let t = td j Calculate tb j The formula for (LS) is as follows:
Figure GDA0003915057640000062
wherein tw j Represents the operating time of vessel j;
s4: inserting a buffer area;
s41: updating the weighting factor w j (ii) a The weighting factor represents the service priority of the ship, and if the weight coefficient exists, the calculated tb is used for j j (ES) and tb j Time and space conflicting vessels j' in the (LS) scheme, i.e. { x j ＝x j' ,tb j' (ES)＜tb j (ES)＜tb j' (LS)+tw j' If j' belongs to V }, then w j Set to 1, otherwise set to 0, where the set V = {1,2, \8230;, n };
s42: calculating the accumulated weight; calculating two key parameters alpha j 、β j The cumulative weight α of the ship j in the same berth and the ship in the previous port j And the cumulative weight beta of the ships at the port of the berth behind j ；
In the berth shore bridge scheme, not only the front and rear ships in transition but also other ships sharing the same wharf space need to be considered; thus, if the definition set Fa (j) records the ship berthing at the same berth as the ship j and berthing ahead of the ship, the definition set Fb (j) records the ship berthing at the same berth as the ship j and berthing behind the ship, and the definition W is used as the total weight of all the ships, then
Figure GDA0003915057640000071
Calculating alpha j And beta j The formula of (1) is as follows:
Figure GDA0003915057640000072
s43: obtaining a more robust berth shore bridge scheme; finally obtaining the berthing time tb of the ship inserted into the buffer area j From tb j (ES)、tb j (LS)、α j 、β j Obtaining:
Figure GDA0003915057640000073
s5: self-adaptive variation of particles; the PSO algorithm has strong global search capability and memorability, has strong optimization capability in the early stage of iteration, but inevitably falls into a local trap in the later stage of iteration, and is difficult to jump out of a local optimal solution to find a global optimal solution, so that aiming at the characteristics of the PSO algorithm and a constructed berth shore bridge problem model, the following adaptive variation strategy is designed to improve the traditional PSO algorithm, and the updating formula of the adaptive variation probability P is as follows:
Figure GDA0003915057640000074
wherein TN is the current iteration frequency, and TN is the total iteration frequency; for the particle i, randomly generating a random number between 0 and 1, and if the random number is greater than the variation probability of the iteration, performing variation operation on the particle;
s51: the mutation strategy is designed with two types of exchange and reverse order respectively, specifically as follows: randomly selecting two columns for exchange; and (3) reversing: randomly selecting two columns from the sample, and arranging the parts including the two selected columns and the parts between the two selected columns in a reverse order, as shown in FIG. 2;
s6: calculating an objective function value of the sample; namely the time of delay departure of the ship, the formula is as follows:
Figure GDA0003915057640000075
s7: updating the individual optimal value and the global optimal value of the particle; for each particle, comparing the fitness value obtained by the iteration with the optimal fitness value pbest, if the fitness value is smaller than pbest, updating, and otherwise, keeping pbest unchanged; comparing pbest with the global optimum value gbest, and if the pbest is smaller than the gbest, replacing the gbest with the pbest;
s8: and updating the speed and the position of the particle, wherein the speed updating formula of the ith particle is as follows:
v ij (tn+1)＝wv ij (tn)+c 1 r 1j (p ij -x ij (tn))+c 2 r 2j (g j -x ij (tn)),j∈V
the location update formula is: x is the number of ij (tn+1)＝x ij (tn)+v ij (tn+1),j∈V
Wherein v is ij (tn + 1) represents the j-dimension velocity value of the tn +1 th iteration particle i, w is a weight coefficient, c 1 And c 2 Is a learning factor, r 1j And r 2j Is a chaotic variable based on Logistic chaotic sequence, p ij Is the j-th dimension position value, g, of the optimal solution of the particle i j Position value of j dimension, x, being global optimum solution ij (tn) represents a j-dimensional position value of the particle i at the tn-th iteration; for the particles with updated speed and positions, carrying out boundary processing on the particles so that the codes of the particles meet the constraint;
s9: and (5) enabling TN = TN +1, judging whether a termination condition of reaching the maximum iteration time TN is met, if so, terminating iteration and outputting an optimal solution, otherwise, returning to the step S2 and continuing iteration.
Example 1: considering the actual working condition of the container terminal, the method formulates a berth shore bridge distribution scheme in advance according to the ship information (such as the number of ships, estimated arrival time, estimated departure time, box carrying capacity and the like) planned to berth at a port and the terminal equipment information (such as the number of berths, the berth length and the total number of shore bridges); for each ship, the following three arrangements should be made: the first is berthing time, the second is berthing, and the third is the number of allocated shore bridges.
The following sets, parameters and variables are set:
b: a berth set of the wharf along a shoreline, i ∈ B = (1, 2,.., m };
v: set of ships arriving port, j ∈ V = (1, 2,.., n };
VL j : safe length of vessel j (including safe distance);
t: planning period, t being unit time index
TN: the iteration times of the cross entropy algorithm, tn is the index of times
QL i : the length of dock i;
r: the working efficiency of the shore bridge;
q: the number of shore bridges on the shore line;
P j : a preferred berth for ship j;
ta j : estimated time to arrival of ship j;
tde j : estimated departure time for ship j;
N j : the number of containers carried by ship j;
Figure GDA0003915057640000091
the minimum required number of shore bridges for ship j;
Figure GDA0003915057640000092
the number of shore bridges required by the ship j at most;
N j : the number of containers carried by ship j;
x j : berthing of the ship j;
y j : the number of shore bridges allocated to ship j;
O j : berthing sequence of vessel j;
tb j : berthing time of ship j;
td j : the departure time of ship j;
tw j : the operating time of vessel j;
s ijk : if the ship j is berthed on the kth berth i, the berth is 1, and if not, the berth is 0;
s jt : if the ship j is served at the time t, the ship j is 1, otherwise the ship j is 0;
the invention aims at minimizing the delay departure time of the ship, and the established optimization model is as follows:
Figure GDA0003915057640000093
constraint conditions are as follows:
Figure GDA0003915057640000101
Figure GDA0003915057640000102
Figure GDA0003915057640000103
Figure GDA0003915057640000104
Figure GDA0003915057640000105
Figure GDA0003915057640000106
Figure GDA0003915057640000107
Figure GDA0003915057640000108
Figure GDA0003915057640000109
Figure GDA00039150576400001010
Figure GDA00039150576400001011
Figure GDA00039150576400001012
the constraint condition (2) indicates that the ship can only berth after arriving at port, the constraint condition (3) indicates that the ship can only berth at a berth larger than the ship length, the constraint condition (4) indicates that the ship has only one berthing opportunity, the constraint condition (5) indicates that one berth serves at most one ship at the same time, the constraint condition (6) indicates that the number of shore bridges allocated to the ship is within a given range, the constraint condition (7) ensures the continuity of the operation of the ship, the constraint condition (8) defines the operating time of the ship, the constraint condition (9) defines the departure time of the ship, and the constraint condition (10) indicates that the number of the shore bridges operated at any time can not exceed the total number of the shore bridges. The constraints (11) - (13) define the value ranges of variables related to decision variables. According to the technical scheme, the berth shore bridge allocation problem is solved, and a final allocation scheduling scheme can be obtained.
And (3) experimental verification:
in order to verify the effectiveness and robustness of the IPSO method for solving the berth shore bridge distribution problem, the length of a shore line is 1200m,4 berths, the lengths of 1-4 berths are respectively 200m,300m and 400m, the unit length is 20m, the unit time t =5min,12 shore bridges are arranged, the working efficiency of the shore bridge is 3.33TEU/t, the estimated arrival time ta is randomly generated within [0,288], the ship length is randomly generated between [6,20], the parameter design of a ship is shown in the following table, the working time is recorded as tw, and the estimated departure time is randomly generated between [ ta + tw +60 ].
TABLE 1 Ship parameter settings
Class of ship Captain of ship Number of containers Range of shore bridge
Small boat [6,10] [800,1500] [1,2]
Middle ship [11,15] [1500,2500] [2,4]
Large ship [16,20] [2500,4000] [3,6]
Recording a berth shore bridge distribution scheme obtained by a traditional method as S1, and recording berthing time corresponding to the scheme S1 as tb j (ES), recording the robust berth shore bridge allocation scheme S2 after the buffer is inserted, and recording the berthing time corresponding to the scheme S2 as tb j . For simulating a real scene, the robustness of the method is tested, and the actual working time is enabled to be [ tw,1.1tw]Internally randomly generating, if a ship can not work by berthing due to the delay of the departure time of the previous ship at the expected berthing time, waiting to the departure time of the previous ship and having enough shore bridges to ensure the berthing of the ship after the work, wherein the actual berthing time is tb a
The invention generates 10 ships with different scales, and compares and obtains the performance of two robustness indexes, namely ship berthing delay time and delay quantity, under 200 random scenes, wherein the specific indexes are as follows:
index 1: sum of delay time of berthing of ship:
Figure GDA0003915057640000111
Figure GDA0003915057640000112
Figure GDA0003915057640000113
wherein, Δ t (S1) represents the sum of S1 delay berthing time, Δ t (S2) represents the sum of S2 delay berthing time, and tIR is the improvement rate of index 1.
Index 2: number of berthing delays of ship:
Figure GDA0003915057640000121
Figure GDA0003915057640000122
Figure GDA0003915057640000123
wherein, delta n (S1) is the sum of S1 delay berth quantity, and delta n (S2) is the sum of S2 delay berth quantity; the improvement rate of index 2 is nIR.
At 10 scales, 200 scenes were randomly generated at each scale, the experimental results are shown in table 2, and fig. 2 shows the comparison of index 1 and index 2 at 10 scales:
TABLE 2 results of the experiment
Number of ships n Δt(S1) Δt(S2) tIR Δn(S1) Δn(S2) nIR
8 63.70 29.94 53.00 5.02 1.91 61.95
9 79.43 34.42 56.67 6.23 2.01 67.74
10 102.82 48.96 52.38 7.09 2.85 59.80
11 136.03 64.20 52.80 8.09 2.93 63.78
12 162.77 73.39 54.91 9.21 3.23 64.93
13 196.08 102.81 47.57 10.09 3.93 61.05
14 233.29 125.24 46.32 11.12 4.28 61.51
15 271.49 129.76 52.20 11.94 4.37 63.40
16 333.53 176.68 47.03 13.06 5.42 58.50
17 347.56 168.54 51.51 14.11 5.42 61.59
As can be seen from table 2, under different calculation examples of the number of ships, Δ t (S2) is always significantly better than Δ t (S1) in index 1, and as can be seen from fig. 2 (a) and (b), as the number of ships increases, Δ t (S1) and Δ t (S2), Δ n (S1) and Δ n (S2) are all in an upward trend, and as can be seen from fig. 2 (c) and (d), as the number of ships increases, values of ttir and nIR are in a slightly downward trend, because as the number of ships increases, the time of delay in berthing and the number of ships increase inevitably, but the improvement rates of both indexes are higher, so the improved particle swarm algorithm provided by the present invention can effectively reduce the delay time and the number of actual berthing of the shore bridge scheme.
The above examples only show some embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention.

Claims (2)

1. A robust berth shore bridge joint distribution method based on an improved particle swarm optimization is characterized in that: the method comprises the following specific steps:
s1: initializing a population; the method specifically comprises the steps of population scale, iteration times, upper and lower bounds of particle positions and speeds, inertia weight and learning factors;
s2: calculate the earliest berthing time tb j (ES): for vessel j, calculate tb j The formula (ES) is as follows:
Figure FDA0003929783090000011
wherein s is ijk The k-th berthing of the ship j at the berth i is 1, otherwise, the k-th berthing is 0 j Represents the time of arrival, td, of vessel j j′ Represents the departure time of vessel j' at berth i;
s3: calculating the latest berthing time tb j (LS): for the ship j, if the ship j' exists and is berthed at the same berth and is berthed at the next berth, let t = tb j′ (LS) if no such ship exists, let t = td j Calculate tb j The formula for (LS) is as follows:
Figure FDA0003929783090000012
wherein tw j Represents the working time of the ship j;
s4: inserting a buffer area; the method comprises the following specific steps:
s41: updating the weighting factor w j (ii) a The weighting factor represents the service priority of the ship, and if the weight coefficient exists, the calculated tb is used for j j (ES) and tb j In the (LS) scheme there are time and space conflicting vessels j', w j Set to 1, otherwise set to 0;
s42: calculating the accumulated weight; calculating the cumulative weight alpha of the ship j in the same berth j And the cumulative weight beta of the ships at the port of the berth behind j ；
Defining set Fa (j) to record the ship berthing at the same berth as the ship j and berthing in front of the ship, defining set Fb (j) to record the ship berthing at the same berth as the ship j and berthing behind the ship, defining W as the total weight of all the ships, then
Figure FDA0003929783090000013
Calculating alpha j And beta j The formula (c) is as follows:
Figure FDA0003929783090000021
s43: finally obtaining the berthing time tb of the ship inserted into the buffer area j From tb j (ES)、tb j (LS)、α j 、β j Obtaining:
Figure FDA0003929783090000022
s5: self-adaptive variation of particles; the following adaptive mutation strategy is designed to improve the traditional PSO algorithm, and the updating formula of the adaptive mutation probability P is as follows:
Figure FDA0003929783090000023
wherein TN is the current iteration frequency, and TN is the total iteration frequency; randomly generating a random number between 0 and 1 for the particle i, and if the random number is greater than the mutation probability of the iteration, performing mutation operation on the particle;
s6: calculating an objective function value of the sample; namely the time of delay departure of the ship, the formula is as follows:
Figure FDA0003929783090000024
s7: updating the individual optimal value and the global optimal value of the particle; for each particle, comparing the fitness value obtained by the iteration with the optimal fitness value pbest, if the fitness value is smaller than pbest, updating, and otherwise, keeping pbest unchanged; comparing the pbest with the global optimal value gbest, and if the pbest is smaller than the gbest, enabling the pbest to replace the gbest;
s8: and updating the speed and the position of the particle, wherein the speed updating formula of the ith particle is as follows:
v ij (tn+1)＝wv ij (tn)+c 1 r 1j (p ij -x ij (tn))+c 2 r 2j (g j -x ij (tn)),j∈V
the location update formula is: x is the number of ij (tn+1)＝x ij (tn)+v ij (tn+1),j∈V
Wherein v is ij (tn + 1) represents the j-dimension velocity value of the tn +1 th iteration particle i, w is a weight coefficient, c 1 And c 2 Is a learning factor, r 1j And r 2j Is a chaotic variable based on Logistic chaotic sequence, p ij Is the j-th dimension position value, g, of the optimal solution of the particle i j Position value of j dimension, x, being global optimum solution ij (tn) represents a j-dimensional position value of the particle i at the tn-th iteration; for the particles with updated speed and positions, carrying out boundary processing on the particles so that the codes of the particles meet the constraint;
s9: and (5) letting TN = TN +1, judging whether a termination condition of reaching the maximum iteration number TN is met, if so, terminating iteration and outputting an optimal solution, otherwise, returning to the step S2 and continuing iteration.
2. The robust berth shore bridge joint distribution method based on the improved particle swarm optimization as claimed in claim 1, wherein: the mutation strategy in S5 is designed with two types, namely, crossover and reverse order, specifically as follows: randomly selecting two columns for exchange; and (3) reversing: two columns are randomly selected from the sample, and the parts including the selected two columns and the parts between the two columns are arranged in the reverse order.
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